The paper is devoted to the 2D hydrodynamical modeling and numerical approximation of an estuarian river flow. A new 2D horizontal model is derived and analyzed as a conforming approximation of the 3D time-discretized problem. It provides the three-dimensional velocity field as well as the pressure, which remains an unknown of the problem. Thanks to the framework of weak formulations, we avoid ...

The paper deals with output feedback regulation of exponentially stable systems by an integral controller. We have recently proposed appropriate Lyapunov functional to prove exponential stability the closed-loop system. approach is dedicated in this hyperbolic and especially de Saint-Venant equations giving explicitly gains ensure stabilized controller: parameters expression deduced directly ba...

We present a splitting method for the one-dimensional Saint-Venant-Exner equations used describing bed evolution in shallow water systems. adapt flux vector approach of Toro and Vazquez-Cend\`on identify one subsystem conservative (advection system) non-conservative (pressure system), both having very simple eigenstructure compared to full system. The final numerical scheme is constructed using...

We study the asymptotic behavior of solutions to variational inequalities with pointwise constraint on the value and gradient of the functions as the domain becomes unbounded. First, as a model problem, we consider the case when the constraint is only on the value of the functions. Then we consider the more general case of constraint also on the gradient. At the end we consider the case when th...

linear control system, 51-67Cauchy problem, 52-54controllability, 55-62Korteweg-de Vries equation, 65—67transport equation, 62-65adjoint operator, 373a d ^ y (definition), 130admissibility condition, 52, see also regularity propertyapproximate controllability, 55, 57, 61Ascoli's theorem, 152, 170attractor, 280averaging, 332-333 backstepping, 334-337, ...